Backlund Transformations in 10D susy Yang-Mills Theories

TL;DR

This paper derives a Bäcklund transformation for ten-dimensional super Yang-Mills equations, extending integrability techniques and connecting to previous work on supersymmetric gauge theories.

Contribution

It introduces a new Bäcklund transformation for 10D super Yang-Mills equations based on gauge transformations satisfying nonlinear conditions.

Findings

Derived a Bäcklund transformation for 10D super Yang-Mills equations.

Showed the transformation preserves the form of the equations.

Connected the transformation to previous integrability methods in supersymmetric theories.

Abstract

This is a continuation of hep-th/9811108, hep-th/9903218, hep-th/9910235, on exact integration technics for modified dynamical equations in ten dimensional supersymmetric gauge theory. A B\"acklund transformation is derived for the Yang type (super) equations previously derived (hep-th/9811108) by M. Saveliev and the author, from the ten dimensional super Yang-Mills field equations in an on-shell light cone gauge. It is shown to be based upon a particular gauge transformation satisfying nonlinear conditions which ensure that the particular form of the equations is retained. These Yang type field equations are shown to be precisely such that they automatically provide a solution of these conditions. This B\"acklund transformation is similar to the one proposed by A. Lesnov for self-dual Yang-Mills in four dimensions. In the introduction a personal recollection on the birth of supersymmetry is given.